The Gau-Gau model of Section 2.1 is a special case of the more general Bayesian hierarchical model (BHM), which is used to denote models that are constructed via the specification of multiple conditional distributions. To the best of our knowledge, the first work that utilised a Bayesian hierarchical model with more than two levels in a glaciological context is that of [1]}. In this work, the model is couched within a physical-statistical modelling framework [2]}, [3]}, and it is used to infer three processes: glacial surface velocity, basal topography, and surface topography, from noisy and incomplete data. The physical-statistical BHM they used is broken up into three models: a data model, a process model, and a parameter model:
